An Algebra Structure for the stable Khovanov homology of torus links

Abstract

The family of negative torus links $T_{p,q}$ over a fixed number of strands $p$ admits a stable limit in reduced Khovanov homology as $q$ grows to infinity. In this paper, we endow this stable space with a bi-graded commutative algebra structure. We describe these algebras explicitly for $p=2,3,4$. As an application, we compute the homology of two families of links, and produce a lower bound for the width of the homology of any $4$-stranded torus link.